Problem: The grades on a history midterm at Loyola are normally distributed with $\mu = 76$ and $\sigma = 5.5$. William earned a n $83$ on the exam. Find the z-score for William's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for William's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{83 - {76}}{{5.5}}} $ ${ z \approx 1.27}$ The z-score is $1.27$. In other words, William's score was $1.27$ standard deviations above the mean.